• Conditional probability, Independence, and Bayes’ Rule
• Use of Venn diagrams and probability trees to visualize probability problems
• Discrete random variables and distributions: Bernoulli, categorical, binomial, geometric, Poisson
• Continuous random variables and distributions: uniform, exponential, normal (Gaussian), Laplace, Gamma, Beta
• Cumulative distribution functions (CDFs), probability mass functions (PMFs), probability density functions (PDFs)
• Joint, marginal, and conditional distributions
• Multivariate distributions, random vectors
• Functions of random variables, sums of random variables, convolution
• Expected values, expectation, mean, and variance
• Skewness, kurtosis, and moments
• Covariance and correlation, covariance matrix, correlation matrix
• Moment generating functions (MGF) and characteristic functions
• Key inequalities like Markov, Chebyshev, Cauchy-Schwartz, Jensen
• Convergence in probability, convergence in distribution, almost sure convergence
• Law of large numbers and the Central Limit Theorem (CLT)
• Applications of probability in machine learning, data science, and reinforcement learning

Common scenario: You try to get into machine learning and data science, but there’s SO MUCH MATH.

Either you never studied this math, or you studied it so long ago you’ve forgotten it all.

What do you do?

Well my friends, that is why I created this course.

Probability is one of the most important math prerequisites for data science and machine learning. It’s required to understand essentially everything we do, from the latest LLMs like ChatGPT, to diffusion models like Stable Diffusion and Midjourney, to statistics (what I like to call “probability part 2”).

Markov chains, an important concept in probability, form the basis of popular models like the Hidden Markov Model (with applications in speech recognition, DNA analysis, and stock trading) and the Markov Decision Process or MDP (the basis for Reinforcement Learning).

Machine learning (statistical learning) itself has a probabilistic foundation. Specific models, like Linear Regression, K-Means Clustering, Principal Components Analysis, and Neural Networks, all make use of probability.

In short, probability cannot be avoided!

If you want to do machine learning beyond just copying library code from blogs and tutorials, you must know probability.

This course will cover everything that you’d learn (and maybe a bit more) in an undergraduate-level probability class. This includes random variables and random vectors, discrete and continuous probability distributions, functions of random variables, multivariate distributions, expectation, generating functions, the law of large numbers, and the central limit theorem.

Most important theorems will be derived from scratch. Don’t worry, as long as you meet the prerequisites, they won’t be difficult to understand. This will ensure you have the strongest foundation possible in this subject. No more memorizing “rules” only to apply them incorrectly / inappropriately in the future! This course will provide you with a deep understanding of probability so that you can apply it correctly and effectively in data science, machine learning, and beyond.

Are you ready?

Let’s go!

Suggested prerequisites:

• Differential calculus, integral calculus, and vector calculus

• Linear algebra

• General comfort with university/collegelevel mathematics

Who this course is for:

• Python developers and software developers curious about Data Science
• Professionals interested in Machine Learning and Data Science but haven’t studied college-level math
• Students interested in ML and AI but find they can’t keep up with the math
• Former STEM students who want to brush up on probability before learning about artificial intelligence